
<A NAME=LaguerreP>

<TITLE>LaguerreP</TITLE></A>
<b><a href=r37_idx.html>INDEX</a></b><p><p>



<B>LAGUERREP</B> _ _ _  _ _ _  _ _ _  _ _ _ <B>operator</B><P>
<P>
 
The <em>LaguerreP</em> operator computes the nth Laguerre Polynomial. 
The two argument call of LaguerreP is a (common) abbreviation of 
LaguerreP(n,0,x). 
<P>
<P>
 <P> <H3> 
syntax: </H3>
<em>LaguerreP</em>(&lt;integer&gt;,&lt;expression&gt;) or 
<P>
<P>
<em>LaguerreP</em>(&lt;integer&gt;,&lt;expression&gt;,&lt;expression&gt;) 
<P>
<P>
<P>
 <P> <H3> 
examples: </H3>
<P><PRE><TT>
LaguerreP(3,xx); 

       3        2
  (- xx   + 9*xx   - 18*xx + 6)/6



LaguerreP(2,3,4); 

  -2

</TT></PRE><P>Laguerre polynomials are computed using the recurrence relation: 
<P>
<P>
LaguerreP(n,a,x) := (2n+a-1-x)/n*LaguerreP(n-1,a,x) - 
 (n+a-1) * LaguerreP(n-2,a,x) with 
<P>
<P>
LaguerreP(0,a,x) := 1 and LaguerreP(2,a,x) := -x+1+a 
<P>
<P>
<P>
